$5.$ Individual Problems $14-2$

A local Pilates studio recently began offering a monthly subscription service for its patrons.

Suppose a particular patron $at$ this studio has the following willingness$-to-$pay schedule, per session.

Session

Willingness $to$ Pay

$1st$ $$105$

$2nd$ $$90$

$3rd$ $$75$

$4th$ $$60$

$5th$ $$45$

$6th$ $$30$

Suppose this consumer would not demand any more sessions, even for free. Also assume that the marginal cost $to$ the studio, per session, $is$ constant $at$ $$15.$

$At$ a price $of$ $$97\mathrm{.}50$ per session, the number $of$ sessions demanded $by$ this consumer would $be.At$ this price and quantity, consumer surplus $is$ and producer surplus $is.$

Suppose the studio has devised a new pricing scheme for consumers who demand more than $1$ session. This pricing scheme $is$ a subscription service, whereby consumers can pay a flat fee $of$ $$324\mathrm{.}00$ and can have $upto6$ sessions total.

Using this subscription pricing model, this consumer would demand sessions. Under this scenario, consumer surplus isand producer surplus $is.(Hint$: For consumer surplus, consider how much total value the consumer places $on$ all sessions, versus the total price paid.$)$